• Mathematician Chat v. 3.999...
    1,232 replies, posted
So, I haven't touched a whole lot of maths since I left school last year aside from my normal calculating service calls for work every day. Does anyone know of a website or a blog where someone posts a few (or just one or two good) algebra/calculus questions/quizes daily that I could use just to warm up my brain over time and get back in the groove of maths?
So we're looking at applications of Fourier Series to PDEs in class and I was hoping someone can have a look over my attempt at a problem to see if I'm not getting it wrong somewhere. To avoid desecrating the Emperor's Palace with my LaTeX, I uploaded the pdf instead. [url]https://www.sendspace.com/file/0ilrgp[/url]
How do calculators do trigonomtery? Of course sin x = o/h but obviously the calculator does not know those values.
I wondered this myself recently, most series converge too slowly to be of any use. For trig functions it uses a fancy rotation algorithm: [url]http://en.wikipedia.org/wiki/CORDIC[/url] Pretty danm smart imho...
Has any of you played with Hidden Markov Models? I wrote an AI today that uses the Baum-Welch algorithm to estimate transition and emission parameters based on a sequence of observations it makes. Seems like it can be applied in countless of areas. I'm thinking about just messing around a bit with it and maybe let it learn some stock data :v:
[QUOTE=arbio22;46219317]How do calculators do trigonomtery? Of course sin x = o/h but obviously the calculator does not know those values.[/QUOTE] My guess is it does a Taylor Series expansion to some arbitrary number of terms.
[QUOTE=Swebonny;46227886]Has any of you played with Hidden Markov Models? I wrote an AI today that uses the Baum-Welch algorithm to estimate transition and emission parameters based on a sequence of observations it makes. Seems like it can be applied in countless of areas. I'm thinking about just messing around a bit with it and maybe let it learn some stock data :v:[/QUOTE] The closest related thing I did was implement a neural network (and another one in CUDA), I also wanted to make one that learns to predict world cup matches but it was implemented in Matlab and matlab sucks balls when it comes to text processing so I gave up :v:
[QUOTE=Swebonny;46227886]Has any of you played with Hidden Markov Models? I wrote an AI today that uses the Baum-Welch algorithm to estimate transition and emission parameters based on a sequence of observations it makes. Seems like it can be applied in countless of areas. I'm thinking about just messing around a bit with it and maybe let it learn some stock data :v:[/QUOTE] Our professor mentioned that we will learn it. I hope it is already this year :)
I feel like I've stepped back 5 years or so, taking Intro to Discrete because it's a pre-req for a required course for my new major. This is basic logic shit, I don't even understand how any of this is remotely difficult. Even the proofs are piss-easy, you just have to do a little bit of lateral thinking and/or trial and error.
my shool's library had an original first edition of descarte's discourse de la methode on display along with several other rare corner-stone writings on math and geometry
I was browsing wikipedia and found that interestingly the integral symbol varies around the world. [IMG]http://puu.sh/ce0se/fbcdb9ab1d.png[/IMG] Good thing I don't have to learn those foreign notations since everyone just uses English.
[QUOTE=Falubii;46246050]I was browsing wikipedia and found that interestingly the integral symbol varies around the world. [IMG]http://puu.sh/ce0se/fbcdb9ab1d.png[/IMG] Good thing I don't have to learn those foreign notations since everyone just uses English.[/QUOTE] With my handwriting i usually end up using all three of those
I heard that Mathematics is the language of the universe. What's it like, speaking to the stars?
Well, if geek shirts are to be considered as canon, God did say: [img]http://www.irregularwebcomic.net/annotations/annot1420a.gif[/img] And now we have light. So we can, almost, talk with God.
well [t]http://rlv.zcache.com/black_and_white_pi_symbol_coaster-r55ac8eba8cc74b8a88df6ec45e9c6234_ambkq_8byvr_512.jpg[/t] is the holiest of universal relationships
And the tastiest.
i like to think pythagoras was sort of a 1-hit wonder, he came up with the great theorem about triangles that probably was independently discovered elsewhere, but then he went on to make a religion about it [editline]16th October 2014[/editline] [url]http://en.wikipedia.org/wiki/Pythagoreanism[/url]
[QUOTE=mastoner20;46256723]Well, if geek shirts are to be considered as canon, God did say: [img]http://www.irregularwebcomic.net/annotations/annot1420a.gif[/img] And now we have light. So we can, almost, talk with God.[/QUOTE] I'd like to think God would be much more elegant than that! Hopefully he'd say something like: [IMG]http://i58.tinypic.com/oprajc.png[/IMG] or [IMG]http://i61.tinypic.com/24l4tap.png[/IMG] and then there would be light. [editline]16th October 2014[/editline] Or something even more amazing that includes magnetic monopoles (which totally definitely exist don't let whiny experimentalists tell you otherwise) using fiber bundles but I haven't read enough Nakahara to make it look nice and elegant yet.
[QUOTE=JohnnyMo1;46256944]I'd like to think God would be much more elegant than that! Hopefully he'd say something like: [IMG]http://i58.tinypic.com/oprajc.png[/IMG] or [IMG]http://i61.tinypic.com/24l4tap.png[/IMG] and then there would be light. [editline]16th October 2014[/editline] Or something even more amazing that includes magnetic monopoles (which totally definitely exist don't let whiny experimentalists tell you otherwise) using fiber bundles but I haven't read enough Nakahara to make it look nice and elegant yet.[/QUOTE] God doesn't know tensor calculus.
a question on hand-writing notes using mathematic notation: how important is it to have neat and tidy handwriting? i try hard to make everything correct but it takes time but writing it uglily is even worse so idk
[QUOTE=arbio22;46219317]How do calculators do trigonomtery? Of course sin x = o/h but obviously the calculator does not know those values.[/QUOTE] Explaining the technical implementations is something you'd find in a 4th year numerical analysis course in compsci, but long story short it uses algorithms such as this one: [url]http://en.wikipedia.org/wiki/CORDIC[/url]
[QUOTE=ZeFruitNazi;46258091]a question on hand-writing notes using mathematic notation: how important is it to have neat and tidy handwriting? i try hard to make everything correct but it takes time but writing it uglily is even worse so idk[/QUOTE] My math teacher often teased one of my mates who was otherwise brilliant about his horrible writing. He did it jokingly and in a friendly manner (he's a pretty cool teacher) but I suspect it's kind of irritating for the person who corrects your papers. [editline]17th October 2014[/editline] As long as it's legible it's no big deal though.
[QUOTE=ZeFruitNazi;46258091]a question on hand-writing notes using mathematic notation: how important is it to have neat and tidy handwriting? i try hard to make everything correct but it takes time but writing it uglily is even worse so idk[/QUOTE] Not too important as long as you avoid things involving pairs like u and v or rho and p.
Assistance, pls [IMG]http://latex.codecogs.com/gif.latex?%5Cint%20%5Cfrac%7Bsin%5E2x%7D%7Bcos%5E3x%7D%20dx[/IMG]
I googled "blowing up points on a plane." I think I may be on the no-fly list now. [editline]17th October 2014[/editline] Never mess with an algebraic geometer. They blow up families and then come back to make sure they're flat.
While we're at it; [IMG]http://latex.codecogs.com/gif.latex?%5Cint%20%5Cfrac%7Btan%5E3x%20+%20tan%20x%7D%7Btan%5E3%20x+3tan%5E2x+2tanx+6%7D%20dx[/IMG]
Ew. Thoroughly ew.
Haha, yeah, that's what we get. It's good practice for first year students though. The world can't always be stringy.
[QUOTE=JohanGS;46260848]While we're at it; [IMG]http://latex.codecogs.com/gif.latex?%5Cint%20%5Cfrac%7Btan%5E3x%20+%20tan%20x%7D%7Btan%5E3%20x+3tan%5E2x+2tanx+6%7D%20dx[/IMG][/QUOTE] Try and use Bioche's rules (not sure how they're called in English). Basically consider w(x)=f(x)dx -If w(-x)=w(x), consider the variable change t=cosx -If w(π-x)=w(x), consider t=sinx -If w(π+x)=w(x), consider t=tanx -If all these conditions are met, consider t=cos(2x) -If none are, consider t=tan(x/2) Using this and some trig formulas you should be able to transform it into something that's easier to integrate.
We haven't done anything about Bioche, but how would I substitute? [editline]17th October 2014[/editline] Well, a hint from the book is t=tan(x), but I'm not sure on how to proceed
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